In its first set of results since its controversial £3.3 billion stock market flotation in October, the company said operating profits after transformation costs were £430 million in the year to March 30, against £403 million a year earlier.
It said its letters performance was at the better end of expectations, with revenues down 2% to £4.6 billion on a year earlier.
Addressed letter volumes declined by 4% but the trend improved over the year due to stronger economic conditions and one-off impacts such as energy companies writing to customers about price rises.
Parcel revenues increased by 7% but in volume terms the one billion items delivered in the period was flat compared with the previous financial year.
Chief executive Moya Greene said: "The competitive environment on the parcels side is more intense. We are taking steps to remain the leader in this growing market."
As the Universal Service provider, Royal Mail is required to provide access to competitors such as TNT for final mile deliveries.
Ofcom is investigating a complaint from TNT over Royal Mail's decision to change conditions and increase the prices it charges to deliver post collected and pre-sorted by its competitors.
Royal Mail believes an investigation into this complaint will lead to a long period of uncertainty around the prices it charges other postal operators.
Ms Greene called for "timely regulatory action" to prevent the impact of direct delivery competition from undermining the economics of the Universal Service.
She said: "TNT Post UK can cherry-pick easy-to-serve urban areas, delivering easy-to-handle post to homes less frequently than Royal Mail and to no defined quality standard.
"Royal Mail is required to deliver six days a week, overnight, throughout the whole country, to stringent quality standards and at a uniform, affordable tariff.
"Moreover, we are also required to deliver any items TNT Post UK does not consider economic to deliver itself. If TNT Post UK is successful in delivering its stated objectives, this could threaten the fundamental economics of the Universal Service."
Royal Mail continues to expect UK-addressed letter market volumes to decline by 4% to 6% a year, although in the current period it will be helped by this month's European and local elections and economic improvements.
Since 2003, more than 50,000 people have left the UK business, with 12,000 leaving in the last four years. In March, the company launched a consultation with unions on a proposal to achieve a net reduction of 1,300 roles.
Shares opened more than 3% lower, although at 553p the stock is still considerably higher than the 330p valuation placed at the time of the flotation.
An Ofcom spokesman said: "We do not believe that there is presently a threat to the financial sustainability of the universal postal service.
"Ofcom keeps the market under constant close review, examining the future business plans of major operators. We have a duty to secure the Universal Service, and if we identify any future threat we have powers to step in to protect it.
"We would expect Royal Mail to take appropriate steps to respond to the challenge posed by competition, including improving efficiency."
Chris Combemale, executive director of the Direct Marketing Association, which represents the commercial users of Royal Mail, said: "With commercial users accounting for a significant portion of Royal Mail's turnover, healthy profits reflect the buoyant state of UK business.
"The rise of e-commerce has put Royal Mail at the heart of the customer experience, integrating advertising, package delivery and transactional mail with digital channels to breathe new life into marketing mail.
"To sustain this growth, Royal Mail should continue to invest in modernising the business to bring further growth and innovation to its commercial customers."